{"as_of":"2026-08-23T20:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:75275db85e59e765c0c7960cb45911700e8586d51387b31f7149c127b5394aea","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-09T17:34:13.401864Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.07218/citation-record","integrity":"/paper/2607.07218/integrity","json":"/paper/2607.07218/citation-record.json","paper":"/paper/2607.07218"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.428479Z","title":"Handbook of Mathematical Functions","venue":null,"work_id":"6c79731e-6fb4-406f-930f-8f53b7788d81","year":1966},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:bce9923d33110eb52f0ede7deab0dc49f2614c31fb08ea34e168bdedcc478f21","observation_id":"36592da8-726c-4a61-9cad-e60e05c38aec","resolution":{"observed_at":"2026-07-09T17:36:25.429909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/acv-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.485502Z","title":"On the asymptotic behavior of a diffraction problem with a thin layer","venue":null,"work_id":"7d228305-f81a-4780-966a-2cc268f652a1","year":2025},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:8ac59ea6d84b048597800395a564ad5b817dbc8cb8b2c183cbdab15e2ebe4ce1","observation_id":"1c46c20e-57ba-495e-9ac0-f149db7dc09b","resolution":{"observed_at":"2026-07-09T17:36:24.487342Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/23m1572544.url:https://doi.org/10.1137/23m1572544","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.479261Z","title":"On the optimal shape of a thin insulating layer","venue":null,"work_id":"45962599-1d3e-4149-945e-cebe37f741e3","year":2024},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:9af1e424de381a45937f1fc2e205e9740958591f732e5a2479e353150dd95fd4","observation_id":"549eedcf-83a5-4c44-98d1-b47b3cd83d34","resolution":{"observed_at":"2026-07-09T17:36:24.480836Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0294-1449(16)30380-8.url:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.455692Z","title":"Reinforcement problems in the calculus of variations","venue":null,"work_id":"9e93bc58-ffbd-43e1-9dbb-11d653df39c0","year":1986},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:aaa4f92f855e949a8c10184f17e15a9f84be3e56e1b76e9dbe9eab115f27fb3d","observation_id":"e917c36c-8c8c-4374-b1b1-b857498c255d","resolution":{"observed_at":"2026-07-09T17:36:24.457292Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0022-247x(83)90066-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A lower bound for the first eigenvalue of an elliptic operator","venue":"Journal of Mathematical Analysis and Applications","work_id":"04f4e3d5-7754-4866-908a-889c445be38f","year":1983},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:18d6306ef5f17495a4b452d1b5c189f6dbd97e879f29ce86bea3b30f9d4ba812","observation_id":"ddbee6e7-e1ad-4c12-9f50-5143603dba3f","resolution":{"observed_at":"2026-07-09T17:36:24.457112Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.426053Z","title":"Bandle and A","venue":null,"work_id":"df649a96-f33e-4d4c-9ccb-64dc3e9b943a","year":2023},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:a17a6c53791b4e5d62aba63d5feddcb8821a3b6d970204f3982dbc16e99fae15","observation_id":"ec8f4f1d-f051-4bb0-a75c-29fa69c5622f","resolution":{"observed_at":"2026-07-09T17:36:25.427842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s12044-018-0398-z.url:http://dx.doi.org/10.1007/s12044-018-0398-z","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.489700Z","title":"Cross-product of Bessel functions: Monotonicity patterns and functional inequalities","venue":null,"work_id":"74bc0fbd-586d-4d44-82d3-5273ec05101c","year":2018},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:8551b2c1830e9f061e55c6d1b965b285624ee3ff614c0891cbcac70bf339b44a","observation_id":"14cd978e-865c-49e5-a290-4857e4e0aa82","resolution":{"observed_at":"2026-07-09T17:36:24.490944Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.415384Z","title":"Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation","venue":null,"work_id":"5443dc8e-9a2e-4bf3-af2f-c436b10dbf5d","year":2019},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:c768ca0d1813add5c392c6e10d60d7208ea394397a1eda776c23c56569619bc6","observation_id":"89c66284-6ce8-435c-a30b-ea2b14003c33","resolution":{"observed_at":"2026-07-09T17:36:25.417354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.418369Z","title":"Longueurs extrémales et fonctionnelles de domaine","venue":null,"work_id":"e1d66360-ec33-44c6-9ac7-d6ab01a0a1ab","year":1986},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:d6c78128205af0735143d20567b44cab594388af0c01e40e9e785c7d591a882e","observation_id":"b354644a-57e8-4666-869c-a58f6c5970d9","resolution":{"observed_at":"2026-07-09T17:36:25.420134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.421105Z","title":"Reinforcement problems for elliptic equations and variational inequalities","venue":null,"work_id":"48ebf4a1-5c1b-4bf6-91c6-7d06569cde45","year":1980},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:0593ac75f89840c7bdab7f487f352ba8ef627cc23cdf4662ab61ea8737c84ffd","observation_id":"98c3c9ad-7cec-458e-87de-d449ed41761b","resolution":{"observed_at":"2026-07-09T17:36:25.422550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.423450Z","title":"Symmetry breaking for a problem in optimal insulation","venue":null,"work_id":"aaedc622-f3ee-43d1-a7e2-4ecd6e6b6ce4","year":2017},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:bffe853eb1ca7aa0d1a491ac62297ca91a66bdb0916daaf7f52091cd92a36bc1","observation_id":"cc9c28f4-0c11-4db7-ae01-534f98acff35","resolution":{"observed_at":"2026-07-09T17:36:25.425458Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/noti1557","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Two optimization problems in thermal insulation","venue":"Notices of the American Mathematical Society","work_id":"dbdfbff6-f763-4243-8be7-d77296f58afb","year":2017},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:3f7399f6e9f13e2e8bc0c7fd3c44ce82a5603613a68995d59d5e4a2113f1f3b1","observation_id":"b8f67b5a-18e7-43e4-be93-e8ddc41516d9","resolution":{"observed_at":"2026-07-09T17:36:24.483237Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.430471Z","title":"Thin insulating layers: the optimization point of view","venue":null,"work_id":"135f8eeb-ec01-480b-9bdd-bad02da760f3","year":1985},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:63b4069e324d443c2bed1eca6ef3efc855ce64df58ecd97010d5a119a134d17a","observation_id":"94f32d64-005f-4eec-98e6-ecdce5dbb4c8","resolution":{"observed_at":"2026-07-09T17:36:25.432307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.459680Z","title":null,"venue":null,"work_id":"5f536b42-a4e7-4a62-8222-1a66f93ef737","year":1959},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:040240e0c6f9560dca9b4f0931aa460eb77b3978e8e591712c5ba8bc3fca131b","observation_id":"ef9cdc50-f33d-429b-a535-0ca75b68d662","resolution":{"observed_at":"2026-07-09T17:36:25.461018Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.anihpc.2016.09.006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A characterization result for the existence of a two-phase material minimizing the first eigenvalue","venue":"Annales de l Institut Henri Poincaré C Analyse Non Linéaire","work_id":"2cb687f9-9777-4926-bca6-09f6789c8da8","year":2017},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:2655e4e4464d5eae8740dd91998e9d9cf455750910afaa6e894f164dd83144af","observation_id":"505bb32b-2f0c-4238-a992-d3bd6bf7e0bd","resolution":{"observed_at":"2026-07-09T17:36:24.484953Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/140971087.url:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.481586Z","title":"Smoothness Properties for the Optimal Mixture of Two Isotropic Materials: The Compliance and Eigenvalue Problems","venue":null,"work_id":"63b2db2f-e00f-4f31-8966-788e630ddd96","year":2015},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:eb45120e1afa49acd3f4852665eb2a4ea8f7ac1aff807303438579562cda9c39","observation_id":"a9bc776e-be82-4593-90d4-040816c9c03b","resolution":{"observed_at":"2026-07-09T17:36:24.483079Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.461568Z","title":"Minimization of the Ground State for Two Phase Conductors in Low Contrast Regime","venue":null,"work_id":"1da59f45-c804-4462-8c92-949b7079cafe","year":2012},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:ec572df691e83d6f5397f937d555390315f887fc4459c1623f0db94e0617f477","observation_id":"d40de8c8-3340-4924-8662-3829ee7e1702","resolution":{"observed_at":"2026-07-09T17:36:25.462859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"proc/2009034","doi":"10.1051/proc/2009034.url:","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball","venue":null,"work_id":"248e0927-99f7-41bc-9440-9abc031ff3f5","year":2009},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:9b7017b374fb29c278a7966e2a9eaac1b4f1955f2bdd7e9f3db11d8730979fc1","observation_id":"b332c856-c048-4fc9-8f65-bd068afa2248","resolution":{"observed_at":"2026-07-09T17:36:24.466555Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02316974.url:http://dx.doi.org/10.1007/bf02316974","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.473848Z","title":"Extremal eigenvalue problems for two-phase conductors","venue":null,"work_id":"8b25aa6c-0071-4075-9c90-1026442c4bfc","year":1996},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:3c3bcff9317a87c0352daca58da1696710fe4cb6f736c02fd18a3223a7a97d03","observation_id":"edd4f3f3-2220-4521-8165-469664fef407","resolution":{"observed_at":"2026-07-09T17:36:24.475751Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2026.114180","doi":"10.1016/j.engappai.2026.114180","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On the classical reinforcement problem and optimisation","venue":"Engineering Applications of Artificial Intelligence","work_id":"833c9a81-1c20-47eb-8994-2434012c04e1","year":2026},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:843e78d951d0d56fc5491eb47f8ff5b61d500ac772823ee6bb310704bf6a4b1a","observation_id":"b1aaf325-caf3-467e-95f7-476363eaab84","resolution":{"observed_at":"2026-07-09T17:36:24.479114Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2509.22305","last_updated":"2026-04-08T10:53:44Z","snapshot_observed_at":"2026-08-09T17:56:00.296646Z","submitted_at":"2025-09-26T13:05:20Z","title":"Remarks on the reinforcement of the spectrum of an elliptic problem with Robin boundary condition","version":2},"cited_work":{"arxiv_id":"2509.22305","doi":null,"metadata_source":"pith","pith_arxiv_id":"2509.22305","snapshot_observed_at":"2026-07-09T17:36:25.355339Z","title":"Remarks on the reinforcement of the spectrum of an elliptic problem with Robin boundary condition","venue":"math.AP","work_id":"c0c393a4-d86a-47f5-a916-176cc8150a1f","year":2025},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"cited_paper":"/paper/2509.22305","citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:c6b6abc78c432ef5d40c347c2c2be58e9c79b78f7fd3df4fdb904f68186e9e02","observation_id":"0dbdc908-bdaf-4e4c-accc-f69cbf92cc11","resolution":{"observed_at":"2026-07-09T17:36:25.356853Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.452628Z","title":"On variations of the shape Hessian and sufficient conditions for the stability of critical shapes","venue":null,"work_id":"70346300-887d-4714-ac8a-958fa663a1de","year":2002},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:d6d057e2138a3f60d5f6f22a325793b7b6a5ee2359915b31e4ca84f040de1d21","observation_id":"c2186f67-cf69-46e5-aee7-44bce4da5ac6","resolution":{"observed_at":"2026-07-09T17:36:25.454420Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00245-010-9111-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On the Shape Sensitivity of the First Dirichlet Eigenvalue for Two-Phase Problems","venue":"Applied Mathematics & Optimization","work_id":"4c16f668-52fd-4d36-a267-30e9cfa5323b","year":2010},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:3bcd239dd9620f86eba9c993c2917fff766918c4da4e13bd1f8cf88603f46c63","observation_id":"4d318078-985f-4ea8-9bcb-07cb1e20330d","resolution":{"observed_at":"2026-07-09T17:36:24.460123Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.450049Z","title":"Stability in shape optimization with second variation","venue":null,"work_id":"85d5c84a-02a3-42f3-8cff-7741e4db41be","year":2019},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:d5ed510d8e289c300e84b4f8a362c14a88380e9818ab71d3788f9e9ec48a8ca3","observation_id":"34ef4d87-b93f-471d-8125-9883bea3d174","resolution":{"observed_at":"2026-07-09T17:36:25.451930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.455289Z","title":"A Faber-Krahn inequality for Robin problems in any space dimension","venue":null,"work_id":"67cc2030-f7c4-4b3f-a710-ddd77d5c1822","year":2006},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:ebdb312d0633e15467e21fae235d9c12ef85d0a15b62668701bc80be56dcdafc","observation_id":"26c9c950-b201-4308-a5e6-03c45f24099b","resolution":{"observed_at":"2026-07-09T17:36:25.456622Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.457382Z","title":"An optimization problem in thermal insulation with Robin boundary conditions","venue":null,"work_id":"1e91d154-790f-4efe-ba3d-6fe557a99967","year":2021},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:5edbacfba273efcb3f35fa4c65c2451dd2af94b9a4bfa0e266861644f8cf11a7","observation_id":"40313948-ec07-4cdf-b49c-0a0eaadb6d2f","resolution":{"observed_at":"2026-07-09T17:36:25.459093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.02229","last_updated":"2026-07-02T14:29:44Z","snapshot_observed_at":"2026-08-07T18:47:22.091840Z","submitted_at":"2026-07-02T14:29:44Z","title":"Optimal insulation and concentration breaking for nonlinear Robin boundary value problems","version":1},"cited_work":{"arxiv_id":"2607.02229","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.02229","snapshot_observed_at":"2026-07-09T17:36:25.358323Z","title":"Optimal insulation and concentration breaking for nonlinear Robin boundary value problems","venue":"math.AP","work_id":"4b35b326-34af-453c-8f08-f12448dba8dc","year":2026},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"cited_paper":"/paper/2607.02229","citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:715ee0bf044355b052f4c62399264001699a1db08670bcddb878424a947fafbc","observation_id":"586292ad-2a55-4afe-ab5f-67630d39471e","resolution":{"observed_at":"2026-07-09T17:36:25.359778Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00526-025-03009-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Some remarks on optimal insulation with Robin boundary conditions","venue":"Calculus of Variations and Partial Differential Equations","work_id":"f8536d72-ea42-42a8-90c9-f9d4ed3f4ca8","year":2025},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:eeeaad616c1425aeb748aef2d2c4b07966192f1a66f98cf0f59f4144e2914c36","observation_id":"2b60faec-2199-486a-b1bc-e5181200d3f6","resolution":{"observed_at":"2026-07-09T17:36:24.474508Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.443166Z","title":"Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt","venue":null,"work_id":"e85681f7-c792-4537-89af-cc4f233e7230","year":1923},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:53dae2e3a595cf8e709d7704dc15f907f55520a8885f6195d7d8ded3e971bbfd","observation_id":"7959f5c5-99e0-4ba3-8da3-b8dd2fb85ab2","resolution":{"observed_at":"2026-07-09T17:36:25.444829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.445632Z","title":"Reinforcement of the principal eigenvalue of an elliptic operator","venue":null,"work_id":"beb0d69b-a42f-4ea3-8514-251a0040dc34","year":1980},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:2d9fcb5dc19f6b16c2b1d55abe31b4b5960d458e1961fe360f121628843f2eff","observation_id":"7bbe2134-445a-4868-b1f5-3a05e63eb63f","resolution":{"observed_at":"2026-07-09T17:36:25.447110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"ijm/1258138","doi":"10.1215/ijm/1258138472","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Bates, J.H","venue":"Illinois Journal of Mathematics","work_id":"1e861a4a-7da8-475c-9092-95a71ace37e3","year":2005},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:5a2066b11231142f50254e2bf0950552a8f91b12a48e0dd01c7b87d0a604652e","observation_id":"61738bbb-be96-4d26-8098-45c9b585bc2b","resolution":{"observed_at":"2026-07-09T17:36:25.355111Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.439150Z","title":"Henrot and M","venue":null,"work_id":"8c001fc4-457d-44f9-9529-cc37897fccde","year":2018},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:e015b1cc0c398cf806214fba85e74dc331d64c29d5c90d96263c5dd4cd3da3a6","observation_id":"025c8d5d-ff91-4169-ac86-f2fe18579ce5","resolution":{"observed_at":"2026-07-09T17:36:25.440321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11425-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.487903Z","title":"Concentration breaking on two optimization problems","venue":null,"work_id":"e708e2dc-705b-4db4-9561-9e9ebc1b4533","year":2024},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:d46a2bbac388a8d41e7c031bc6e8ae07be363f02e00b6f9795bcd392d357302e","observation_id":"bf7945d8-aa05-4d84-a2e2-47ca781818bc","resolution":{"observed_at":"2026-07-09T17:36:24.489170Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.matpur","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.445589Z","title":"Stability analysis on two thermal insulation problems","venue":null,"work_id":"d953ef4f-4636-4dd6-9769-0d670d0ae4c1","year":2022},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:1a2423f6216935aedb0a00f3f7574dd9ec9c3186d12e4baedb70a7dc9dedd165","observation_id":"6bbb0d61-5f43-48e7-b229-195b60210215","resolution":{"observed_at":"2026-07-09T17:36:24.449733Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.437499Z","title":"Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises","venue":null,"work_id":"5510bcde-4c8a-471c-8b69-6b0ca35e0527","year":1925},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:9d160878ee78be7ceae44d9c3db5d43e5e9b0df025f94edc75e0c1028090e5bf","observation_id":"43cf5dba-c1ae-405e-a8d2-c9440ae8481f","resolution":{"observed_at":"2026-07-09T17:36:25.438951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.440860Z","title":null,"venue":null,"work_id":"7c64484c-90c1-41c3-8b17-1f6717fced86","year":1968},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:16a3d3b906e394a9ee42de924d430383ead0b399ff403ef25534dbc7edf72c34","observation_id":"da240f6f-69cf-4b2e-a916-9661a0713b3e","resolution":{"observed_at":"2026-07-09T17:36:25.442539Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"cocv/2013067","doi":"10.1051/cocv/2013067.url:http://dx.doi.org/10.1051/cocv/2013067","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"Global minimizer of the ground state for two phase conductors in low contrast regime","venue":null,"work_id":"a0caf7f2-4890-448c-8448-de59969e6fc4","year":2014},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:4603028415277e2794cddd6ec2d7f1f82068039d7dd02f95dc9bf02d38637aa2","observation_id":"42cf8da5-a2a1-4831-8e6f-15675db0727b","resolution":{"observed_at":"2026-07-09T17:36:24.478679Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.441022Z","title":"Asymptotic behavior of Robin problem for heat equation on a coated body","venue":null,"work_id":"6d7d31a3-9d16-4bf5-b6ce-ef5d7282274e","year":2012},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:31a8e83366606b8013abf1a0d1be4803669a66c8ac5c71e21afa91c159acb7b1","observation_id":"dcf256de-4512-488f-8dbf-d3457e665aeb","resolution":{"observed_at":"2026-07-09T17:36:25.442230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.435586Z","title":"Shape optimization of a weighted two-phase Dirichlet eigenvalue","venue":null,"work_id":"e10fbb9b-2dca-43ad-b4eb-18e55bd02e66","year":2022},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:fb39a521197415d47d48658026fe9bae2403357f370c11dfeb62347b195b4136","observation_id":"d2d3acf2-3360-4f2b-9006-603b114e7342","resolution":{"observed_at":"2026-07-09T17:36:25.436975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:25.448043Z","title":null,"venue":null,"work_id":"e4d8d45f-b691-4bfb-ae10-39e036fb3ab1","year":1922},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:f33c2589bab9b9e10e74611c13692281f4b42ae59003012697622784a74ed757","observation_id":"6a300aa7-4db1-44dc-a3c7-8979903fb420","resolution":{"observed_at":"2026-07-09T17:36:25.449417Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/00036811","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.467425Z","title":"Asymptotic behavior for the principal eigenvalue of a reinforcement problem","venue":null,"work_id":"185ca3d1-610c-4bfe-895e-539da33c5d7c","year":2018},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:42d3490cade32d39820a15624a4061f70328c5f5f8be15b02efd38832967cce5","observation_id":"a4534219-093a-44bf-b082-3ccc3ede73e1","resolution":{"observed_at":"2026-07-09T17:36:24.469495Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/dcds.2009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.483848Z","title":"Estimating thermal insulating ability of anisotropic coatings via Robin eigenvalues and eigenfunctions","venue":null,"work_id":"074e27d7-b214-4b5d-925f-7c49c77d22cc","year":2009},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:20c34d87fb759b89aaad166c0a0258a4ff84bb240c13d1398261508ca93f91bd","observation_id":"5f6dacf2-4242-42be-93a8-0f62acb6ee54","resolution":{"observed_at":"2026-07-09T17:36:24.485104Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.matpur.2021.07.003.url:http://dx.doi.org/10.1016/j.matpur.2021.07.003","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T17:36:24.465552Z","title":"Regularity of a transmission problem and periodic homogenization","venue":null,"work_id":"a56b864b-127e-4db6-ae4f-f642ea52950e","year":2021},"citing_paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-07-09T17:34:13.401864Z"},"links":{"citing_paper":"/paper/2607.07218"},"observation_digest":"sha256:767e3a80e3e7ce3d399e6f8083e35aca8242f359f17304d497d9bc696b72a369","observation_id":"299e8211-24e8-4c25-9727-594aa133823f","resolution":{"observed_at":"2026-07-09T17:36:24.467095Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.07218","last_updated":"2026-07-08T10:00:46Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-16T20:23:37.618949Z","submitted_at":"2026-07-08T10:00:46Z","title":"Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":3,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":3,"verified_exact":17,"verified_fuzzy":18},"total_outbound_references":43},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2607.07218."}